路与简单扇图联图的(2,1)-全标号

The Total Labelling Number of the Joint Graph of Path and Simple Fan

图G的一个k-(2,1)-全标号是一个映射f:V(G)∪E(G)→{0,1,2,…,k},使得(1)相邻的顶点标不同的号,(2)相邻的边标不同的号,(3)顶点与所关联的边标号数相差至少为2。图G的(2,1)-全标号数定义为G有一个k-(2,1)-全标号的最小的k值,记为λ2T(G)。根据路与扇图联图的特点,找到一种特殊的标号方法,给出路与简单扇图联图的(2,1)-全标号数的上界。

The（2,1）-total labelling number λT2（G） of a graph G is the width of the smallest range of integers that suffices to label the vertices and edges of G such that：（1）any two adjacent vertices of G receive distinct integers,（2）any two adjacent edges of G receive distinct integers,（3）each vertex and its incident edges receive integers that differ by at least 2 in absolute value.By the structure of the joint graph of path and fan,find a good labelling method,some results of（2,1）-total labelling number for the joint of path and simple fan are given.